ceta_equiv: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.2: error below the reduction pair processor
  1.1.2.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
   pairs:
   
   eq#(cons(t, l), cons(t', l')) -> eq#(t, t')
   eq#(cons(t, l), cons(t', l')) -> eq#(l, l')
   eq#(apply(t, s), apply(t', s')) -> eq#(t, t')
   eq#(apply(t, s), apply(t', s')) -> eq#(s, s')
   eq#(lambda(x, t), lambda(x', t')) -> eq#(x, x')
   eq#(lambda(x, t), lambda(x', t')) -> eq#(t, t')
   rules:
   
   and(true, y) -> y
   and(false, y) -> false
   eq(nil, nil) -> true
   eq(cons(t, l), nil) -> false
   eq(nil, cons(t, l)) -> false
   eq(cons(t, l), cons(t', l')) -> and(eq(t, t'), eq(l, l'))
   eq(var(l), var(l')) -> eq(l, l')
   eq(var(l), apply(t, s)) -> false
   eq(var(l), lambda(x, t)) -> false
   eq(apply(t, s), var(l)) -> false
   eq(apply(t, s), apply(t', s')) -> and(eq(t, t'), eq(s, s'))
   eq(apply(t, s), lambda(x, t)) -> false
   eq(lambda(x, t), var(l)) -> false
   eq(lambda(x, t), apply(t, s)) -> false
   eq(lambda(x, t), lambda(x', t')) -> and(eq(x, x'), eq(t, t'))
   if(true, var(k), var(l')) -> var(k)
   if(false, var(k), var(l')) -> var(l')
   ren(var(l), var(k), var(l')) -> if(eq(l, l'), var(k), var(l'))
   ren(x, y, apply(t, s)) -> apply(ren(x, y, t), ren(x, y, s))
   ren(x, y, lambda(z, t)) -> lambda(var(cons(x, cons(y, cons(lambda(z, t), nil)))), ren(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t)))
   
    the pairs 
   eq#(apply(t, s), apply(t', s')) -> eq#(t, t')
   eq#(apply(t, s), apply(t', s')) -> eq#(s, s')
   
   could not apply the generic root reduction pair processor with the following
   SCNP-version with mu = MS and the level mapping defined by 
   pi(eq#) = [(epsilon,0),(1,0)]
   polynomial interpretration over naturals with negative constants
   Pol(eq#(x_1, x_2)) = 1
   Pol(cons(x_1, x_2)) = x_2 + x_1
   Pol(apply(x_1, x_2)) = 1 + x_2 + x_1
   Pol(lambda(x_1, x_2)) = x_2 + x_1
   problem when orienting DPs
   cannot orient pair eq#(cons(t, l), cons(t', l')) -> eq#(t, t') weakly:
   [(eq#(cons(t, l), cons(t', l')),0),(cons(t, l),0)] >=mu [(eq#(t, t'),0),(t,0)] could not be ensured